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Modulational instability and spatial structures of the Ablowitz–Ladik equation

✍ Scribed by Alidou Mohamadou; Ferdinand Fopa; Timoléon Crépin Kofané

Publisher: Elsevier Science
Year: 2006
Tongue: English
Weight: 642 KB
Volume: 266
Category: Article
ISSN: 0030-4018
DOI: 10.1016/j.optcom.2006.05.028

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✦ Synopsis

Spatial structures as a result of a modulational instability are obtained in the integrable discrete nonlinear Schro ¨dinger equation (Ablowitz-Ladik equation). Discrete slow space variables are used in a general setting and the related finite differences are constructed. Analyzing the ensuing equation, we derive the modulational instability criterion from the discrete multiple scales approach. Numerical simulations in agreement with analytical studies lead to the disintegrations of the initial modulated waves into a train of pulses.

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